Folded structures have many advantages over structures produced by other means such as casting, stamping or assembling due to cost of manufacture and versatility as adapted to sheet materials. Among methods for designing folding patterns include simple folding patterns containing planar regions and no internal vertices, for example box pattern with six squares forming a “t”; Origami bases, for example a square origami sheet with multiple pointed legs as the intermediary step for making origami animals and figures; two-dimensional flattened patterns where the sheet is folded back into its original plane, forming multiple layers with various geometries, but no three-dimensional structures are made; and factorable three-dimensional patterns surfaces that reduce into row and column cross sections as described by U.S. Pat. No. 6,935,997 to Kling (hereinafter the “Kling patent”), which is herein incorporated by reference. Material flow and mathematical models in doubly-periodic folding (DPF) structures were described in detail by the Kling patent.
The methods of the Kling patent may be restrictive and another problem with designing doubly periodic folded (DPF) structures, or other folded structures with substantially many fold vertices on the interior not on the boundary or by cut-outs is very difficult due to pleat-angle conditions and other constraints. In addition to the zero-curvature condition enabling foldability, structures are desired having periodicity features, having local facet configuration arrangements, and having overall shapes that are bounded by planar or curved surfaces. Further, designing a curved edge is complicated because its two curved neighboring faces will be curved, it will have a compound curve formed by the intersection of the two faces, and its geodesic curvature from both sides must sum to zero.
Given the above, applicant has found an Aspect Shaping Floating (ASF) method for design and preparation of folded structures.